Question: Simplify; express your answer in exponential form. Assume $n\neq 0, p\neq 0$. $\dfrac{{(n^{-1})^{-5}}}{{n^{-3}p^{4}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(n^{-1})^{-5} = n^{5}}$ In the denominator, we can use the distributive property of exponents. ${n^{-3}p^{4} = n^{-3}p^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(n^{-1})^{-5}}}{{n^{-3}p^{4}}} = \dfrac{{n^{5}}}{{n^{-3}p^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}}}{{n^{-3}p^{4}}} = \dfrac{{n^{5}}}{{n^{-3}}} \cdot \dfrac{{1}}{{p^{4}}} = n^{{5} - {(-3)}} \cdot p^{- {4}} = n^{8}p^{-4}$.